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AleksandrR [38]
2 years ago
13

Choose the equation below that represents the line passes to the point (7,-2) an the slope of -3

Mathematics
1 answer:
katrin [286]2 years ago
8 0
Hello there!
 The answer is c because the equation that is being used is point-slope, which is:
y-y1=m(x-x1)
hope this helps
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Cathy did a survey in four bird parks and wrote the following observations: park p number of green birds 18 total number of bird
Nutka1998 [239]
Park p : 
18/82 = 0.219 = 21.9% green birds

park q :
39/88 = 0.443 = 44.3% green birds

park r :
38/64 = 0.593 = 59.3% green birds

park service :
22/50 = 0.44 = 44%

park with greatest percentage of green birds is park r <==
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2 years ago
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Asaph took out a loan for $17,550. To pay it back, he will make 60 monthly payments of $437.
alexira [117]
Total payments 437×60=26,220
Interest paid
26,220−17,550=8,670
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Simplify y^-2/y^-7. Write your answer with a positive exponent only.
attashe74 [19]

Answer:

y^5

Step-by-step explanation:

y^-2/y^-7

When we divide exponents with the same base, we subtract the exponents

y^ ( -2 - -7)

y^ ( -2+7)

y^ 5

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3 years ago
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A soccer ball kicked from the ground with an initial velocity of 32 ft/s is given by the function
Greeley [361]

Answer:

In words the answer is between t=0 and t=2.

In interval notation the answer is (0,2)

In inequality notation the answer is 0<t<2

Big note: You should make sure the function I use what you meant.

Step-by-step explanation:

I hope the function is h(t)=-16t^2+32t because that is how I'm going to interpret it.

So if we can find when the ball is on the ground or has hit the ground (this is when h=0) then we can find when it is in the air which is between those 2 numbers.

0=-16t^2+32t

0=-16t(t-2)

So at t=0 and t=2

So the ball is in the air between t=0 and t=2

Interval notation (0,2)

Inequality notation 0<t<2

6 0
3 years ago
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For 0 ≤ ϴ &lt; 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va
Black_prince [1.1K]

Answer:

3 solutions:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is tan(\frac{\theta}{2}) so let's focus on that part of the equation first.

We know that:

tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}

therefore:

cos(\frac{\theta}{2})\neq0

so we need to find the angles that will make the cos function equal to zero. So we get:

cos(\frac{\theta}{2})=0

\frac{\theta}{2}=cos^{-1}(0)

\frac{\theta}{2}=\frac{\pi}{2}+\pi n

or

\theta=\pi+2\pi n

we can now start plugging values in for n:

\theta=\pi+2\pi (0)=\pi

if we plugged any value greater than 0, we would end up with an angle that is greater than 2\pi so,  that's the only angle we cannot include in our answer set, so:

\theta\neq \pi

having said this, we can now start solving the equation:

tan(\frac{\theta}{2})=sin(\theta)

we can start solving this equation by using the half angle formula, such a formula tells us the following:

tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}

so we can substitute it into our equation:

\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)

we can now multiply both sides of the equation by sin(\theta)

so we get:

1-cos(\theta)=sin^{2}(\theta)

we can use the pythagorean identity to rewrite sin^{2}(\theta) in terms of cos:

sin^{2}(\theta)=1-cos^{2}(\theta)

so we get:

1-cos(\theta)=1-cos^{2}(\theta)

we can subtract a 1 from both sides of the equation so we end up with:

-cos(\theta)=-cos^{2}(\theta)

and we can now add cos^{2}(\theta)

to both sides of the equation so we get:

cos^{2}(\theta)-cos(\theta)=0

and we can solve this equation by factoring. We can factor cos(\theta) to get:

cos(\theta)(cos(\theta)-1)=0

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

cos(\theta)=0

\theta=cos^{-1}(0)

\theta={\frac{\pi}{2}, \frac{3\pi}{2}}

Equation 2:

cos(\theta)-1=0

we add a 1 to both sides of the equation so we get:

cos(\theta)=1

\theta=cos^{-1}(1)

\theta=0

so we end up with three answers to this equation:

\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}

7 0
2 years ago
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